Aligning shapes and quantizing distances between shapes on the plane grid?
Location and Rotation values for the selected object are editable in the Properties panel : 

Clic on the + on the top right corner of your 3D view or press N. 



You can specify the rotation and translation for x,y,z values.

Tip: you can edit x,y,z values at once. This can be done by clicking on one button and dragging vertically to include buttons above/below. After the vertical motion you can drag from side to side (for finer control use Alt or Ctrl while dragging the mouse), or release the LMB to type in a value and Return. 



Number Buttons reference in Blender Manual